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Posterior Probabilities for a Consensus Ordering

Published online by Cambridge University Press:  01 January 2025

Michael A. Fligner  and
Joseph S. Verducci
Michael A. Fligner
Affiliation:
The Ohio State University
Joseph S. Verducci*
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Joseph S. Verducci, Department of Statistics, 1958 Neil Ave., Columbus, OH 43210-1247.
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Abstract

In the situation where subjects independently rank order a fixed set of items, the idea of a consensus ordering of the items is defined and employed as a parameter in a class of probability models for rankings. In the context of such models, which generalize those of Mallows, posterior probabilities may be easily formed about the population consensus ordering. An example of rankings obtained by the Graduate Record Examination Board is presented to demonstrate the adequacy of these generalized Mallows' models for describing actual data sets of rankings and to illustrate convenient summaries of the posterior probabilities for the consensus ordering.

Keywords

concordanceconsensuspermutationrankingsocial welfare function
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 1 , March 1990 , pp. 53 - 63
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The authors thank Leann Birch for permission to refer to her experiment on cracker preferences, and the Graduate Record Examination Board for permission to use primary data from the Pike Report in our example. We also thank the referees for helpful comments.

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